What is the difference between a machine learning engineer and deep learning engineer?
Job titles in IT are somewhat arbitrary, and not very consistent even within the same country or general industry. Job titles in software development, especially newer forms of software development such as mobile apps, even more so. The latest trends in Data Science, Machine Learning and "AI" are at the sharp end of that. 

There are some common themes - e.g. an AI Researcher is likely to be expected to be up to date with scientific papers and might be expected to produce some (or summaries/applications of same within the work environment) whilst a Deep Learning Engineer might 
be expected to be familiar with the ins and outs of provisioning compute resources in Amazon (AWS) or Google (GCP), moving data around for training or inference, with enough coding experience to integrate a TensforFlow model with some already-existing web service. However, none of this is strictly separated and a job advertised as "Data Scientist" for a smaller company might be expected to do both those things and more.

All this means that your best bet is to not take much notice of the job title. Read the job specification carefully. Approach each company with questions about daily tasks, responsibilities and assumed technical skills. Expect in some cases that the companies will be unsure themselves of what the job entails and expecting you to take a mature role in defining your own working relationship with the rest of the company - the more senior and experienced the role being looked for, the more likely this is. Both sides  - prospective employee and prospective employer - may have incorrect assumptions about what is realistic and possible.

TL;DR: It's a bit Wild West out there at the moment, and likely will remain so over the next decade. To reduce variance in your own experience, research job posts carefully and talk in detail to employers about expectations in advance.